The quantum key distribution theory is to distribute a security key by using two channels, namely a quantum channel and an open channel, and is performed using four processes: quantum transmission, information reconciliation, privacy amplification, and proof. In the quantum transmission process, a security key in a photon form is transmitted through a quantum channel. In this state, a transmitter and a receiver may detect wire-tapping of a pirate listener to minimize his/her influence, and the receiver receives a quantum key influenced by a quantum channel error rate. In addition, the information reconciliation is performed through an open channel, and an error of the quantum key of the receiver is corrected to have the same binary bit sequence as a quantum key of the transmitter. The open channel is a non-error channel (noiseless channel) where no error occurs and is assumed as a channel which cannot be maliciously influenced by a pirate listener. However, since all processes are performed in an open state, a pirate listener may also obtain information about the quantum key. The privacy amplification is a state at which security of the quantum key is enhanced by removing information leaked by a pirate listener at previous processes. Through this process, the length of the quantum key decreases in proportion to the influence of the pirate listener. The proof process should be performed together with all previous processes and checks whether the quantum key generation process is performed by the appointed transmitter and receiver, other than a third party such as a pirate listener.
In the quantum transmission process, the influence of a pirate listener may be stochastically minimized through quantum-mechanical characteristics by using a technique such as BB84, and simultaneously key information may be transmitted safely in comparison to classic security communication techniques. However, in the information reconciliation process through an open channel, the amount of leaked information varies depending on a used protocol, and the number of users of the open channel also gives a great influence on a quantum key generation rate. A cascade protocol and a winnow protocol are representative information reconciliation methods which have been studied until now. The cascade protocol corrects errors using a binary search technique and thus has low complexity, but this has a serious delay problem due to an excessive use of open channels. In addition, the winnow protocol solves the delay problem of the cascade protocol to some extent by using hamming codes to correct errors, but the error correcting process is performed inefficiently. In order to compensate such drawbacks of the bi-directional information reconciliation methods, many techniques have been studied, representatively an information reconciliation protocol using LDPC codes. This protocol may correct errors by using minimal open channels and also have high error correction ability. However, since a fixed amount of information leaks regardless of the quantum channel error rate in the error correction process, information unnecessarily leaks when a quantum channel has a low error rate. On the contrary, when a quantum channel has a high error rate, error correction may be failed due to insufficient error correction ability.
Literatures related to the present disclosure are as follows.
[Literature 1] C. Berrou, A. Glavieux, P. Thitimajshima, “Near shannon limit error—correcting coding and decoding: Turbo-codes(1)”, In proc. IEEE Int'l Conf. on computers, pp. 1064-1070, May 1993.
Literature 1 proposes encoding and decoding structures of turbo codes. In addition, Literature 1 reveals that the turbo codes have excellent error correction ability along with LDPC codes in comparison to other error correction techniques.
[Literature 2] C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proc. IEEE Int'l Conf. on Computers, Systems and Signal, 1984, pp. 175-179.
In Literature 2, basic concepts of the quantum key distribution theory are established, and study results of the BB84 technique for transmitting quantum photons are disclosed.
[Literature 3] G. Brassard, L, Salvail, “Secret key reconciliation by public discussion,” Advances in Cryptology, Eurocypt '93, 1994, pp. 410-423.
Literature 3 proposes Cascade protocol used in public discussion. This is a technique for correcting errors of quantum keys by using a binary search technique.
[Literature 4] W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. H. Nickel, C. H. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A, vol. 87, no. 052303, pp. 1-8, May 2003.
Literature 4 proposes Winnow protocol used in public discussion. This technique is a bi-directional protocol, similar to Cascade, to correct errors by using hamming codes, and the delay problem of Cascade protocol is solved to some extent.
[Literature 5] A. D. Livens, Z. Xiong, and C. N. Georghiades, “Compression of binary sources with side information at the decoder using LDPC codes,” IEEE Commun. Lett., vol. 6, no. 10. pp. 440-442, October 2002.
Literature 5 proposes an information reconciliation protocol LDPC codes. This technique is a one-direction protocol for obtaining information about an error bit by using syndrome information of the LDPC codes, and also performs an error correction process based on the error bit.
[Literature 6] W. Y. Hwang, I. G. Koh, and Y. D. Han, “Quantum cryptography without announcement of bases,” Phys. Lett. A, vol. 224, pp. 489-434, August 2003.
In Literature 6, the principle and effects of the quantum key expansion theory are analyzed. Literature 8 reveals that a transmitter and a receiver are able to expand a size of a quantum key as desired and also enhance the quantum key generation efficiency.